To determine the number of real solutions for the quadratic equation \( 4x^2 + x + 3 = 0 \), we can use the discriminant method. The discriminant \( D \) is calculated using the formula:
\[ D = b^2 - 4ac \]
For the quadratic equation \( ax^2 + bx + c = 0 \), the coefficients are:
- \( a = 4 \)
- \( b = 1 \)
- \( c = 3 \)
Now, we can compute the discriminant:
\[ D = (1)^2 - 4(4)(3) = 1 - 48 = -47 \]
Since the discriminant \( D \) is less than zero (\( D < 0 \)), the quadratic equation has no real solutions.
Therefore, the answer is:
no real solutions
1 answer